Simplify the following expression: $ p = \dfrac{3}{10} + \dfrac{-2}{-2k - 9} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-2k - 9}{-2k - 9}$ $ \dfrac{3}{10} \times \dfrac{-2k - 9}{-2k - 9} = \dfrac{-6k - 27}{-20k - 90} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-2}{-2k - 9} \times \dfrac{10}{10} = \dfrac{-20}{-20k - 90} $ Therefore $ p = \dfrac{-6k - 27}{-20k - 90} + \dfrac{-20}{-20k - 90} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{-6k - 27 - 20}{-20k - 90} $ $p = \dfrac{-6k - 47}{-20k - 90}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{6k + 47}{20k + 90}$